• To construct a box plot
• To interpret data in a box plot

Course 1, Lesson 12-3

Statistics and Probability

• box plot

Course 1, Lesson 12-3

Statistics and Probability

​The measures of variation are in a box plot. The smallest number is the lower extreme/minimum number. The largest number is the upper extreme/maximum number.

• ​Lower Extreme/Minimum

• Upper Extreme/Maximum

• ​The Median may not divide the box in half because the data may be clustered toward one quartile.

• If the length of a whisker or the box is short, the values of the data in that part are concentrated

• If the length of a whisker or the box is long, the values of the data in that part are spread out. ​

• If the data set includes outliers, then the whiskers will not extend to the outliers, just to the previous data point.

• Outliers are represented with an asterisks (*).

​

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Need Another Example?

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Step-by-Step Example

1.

Draw a box plot of the car speed data.

25 35 27 22 34 40 20 19 23 25 30

Order the numbers from least to greatest. Then draw a
number line that covers the range of the data.

Find the median, the extremes, and the first and third
quartiles. Mark these points above the number line.

Draw the box so that it includes the quartile values. Draw a vertical
line through the box at the median value. Extend the whiskers from
each quartile to the extreme data points. Include a title.

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Step-by-Step Example

2.

Half of the drivers were driving faster than what
speed?

Half of the 11 drivers were driving faster than 25 miles
per hour.

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Step-by-Step Example

3.

What does the box plot’s length tell about the data?

The length of the left half of the box plot is short. This
means that the speeds of the slowest half of the cars
are concentrated. The speeds of the fastest half of the
cars are spread out.

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Step-by-Step Example

4.

The box plot below shows the daily attendance at a
fitness club. Find the median and the measures of
variability. Then describe the data.

The median is 72.5. The first quartile is 65 and the third
quartile is 80. The range is 54 and the interquartile range
is 15. There is an outlier at 110. Both whiskers are
approximately the same size so the data, without the
outlier, is spread evenly below and above the quartiles.

• ​If the length of a whisker or the box is short, the values of the data in that part are concentrated.

• If the length of a whisker or the box is long, the values of the data in that part are spread out. ​

• The Box and Whisker plot is divided in to 4 parts.

• Each Part is 25% of the data set or ¼.

Analyzing the Data Set